Vacuum tube circuits



Aug. 14, 1934. R M. KALB 1,970,316

VACUUM TUBE CIRCUITS Filed Jan. 13, 1932 CHANGE IN FUNDAMENTAL AMPLITUDE RATIO THIRD HARMONIC AMPLITUDE LOAD RESISIANCE-l'I-IOUSANDS OF oHM's INVENTOR R. M. KALB AZTORNEV Patented Aug. 14, 1934 UNITED STATES VACUUM TUBE CIRCUITS Robert M. Kalb, East Orange, N. 3., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application January 13, 1932,.Serial No. 586,257 2 Claims. (01. no- 171 V This invention relates to wave translating systems, for example, signaling systems employing electric space discharge amplifying devices.

An object of the invention is to improve the 5 grade of transmission in such systems.

It is also an object of the invention to control gain in such systems, for instance to operate vacuum tubes in such systems so that change of gain with transmission level is controlled as desired. For example, it may be desired that there be substantially no change of gain with transmission level.

As explained in a paper by E. Peterson Impedance of a Non-Linear Circuit Element Transactions of the American Institute of Electrical Engineers, Vol XLVI, pages 528 to 534, 1927, effects of harmonics generated in a vacuum tube, called by him loading and reaction effects, may change the amplitude of the fundamental wave. The harmonics shift the operating region 'on the (non-linear) plate voltage-plate current characteristic of the tube so that the plate impedance in the tube. to the fundamental is changed, and moreover, the harmonics require energy dissipation or storage and dissipation at.

harmonic frequencies, whichf'appea'rs as im- It is possible by such prevention in accordancewith the invention, to operate vacuum tubes so 40 that there is substantially no change of gain with transmission 'level. Such operation is especially advantageous where a large number of tubes are connected in tandem. In such cases, uncontrolled changes of gain with transmission level may be large because of the cumulative action of the large number of repeaters, for example. The changes in gain not only cause distortion of signals, but may result in 5 greater amplification at low levels than at high levels and consequently in decrease of signal-tonoise ratio.

,Other objects and aspects of the invention willbe apparent from the following description and claims.

Fig. l of the drawing shows a vacuum tube amplifier circuit embodying a form of the invention; and

Fig. 2 shows curves facilitating explanation of the invention.

, these harmonics.

In the systemof Fig. l, a vacuum tube 1 am plifies waves from source 2 and transmits them to a load resistance R. The usual cathode heating, grid biasing and plate voltage supply sources are shown. Currentfrom the plate voltage supply source flows through a choke 00115 and is prevented from flowing through resistance R by a stopping condenser 10.

The known fact that there exists a relation be tween the amplitude of the thirdharmonic and the change in fundamental amplitude in the output of a vacuum tube, caused by harmonics, suggests devising a method for determining either from the other- Once the relation is is restricted to one special case which is of limited practical importance, for at load impedances other than zero the ratio of fundamental increment to the amplitude of the third harmonic in general differs greatly from three, as brought out hereinafter. The difference is caused by the change, due to harmonics, of the external impedance to the fundamental, and by change in the diversion of energy from the fundamental to The latter effect (the diversion) is altered by a changein the impedance to 7 any harmonic. As the harmonics are functions of the operating point and load impedance, the increment in the fundamental caused'by'them is in general a function of the same variables.

In taking account of the, loading and reaction effects of harmonics, the effects of the variable amplification factor will also beincluded by following the methods'used by Peterson and Evans in their paper on Modulation in Vacuum Tubes Used as Amplifiersflpublish'ed in Bell System Technical Journal, July, 1927, pp. 442-460." Their nomenclature will also be adopted. For an applied sinusoidal voltage of amplitude P the amplitude of the second harmonic is Cz, and of the third harmonic,

as may be seen by expanding the second and third powers of e=P cos pt in terms of its harmonics and substituting the results for corresponding powers of e in Equation (5) of the paper just mentioned. (In these and following expressions the Csare functions of the impedances of the external plate circuit for the tube and of the parameters of the tube.) When this is done there This is seen to give the constant ratio threebe- V 3 3 2 2 RJ 2 b 3 80 tween fundamental increment and. third har- 30 1 21 l 12 1 03 monic p ud Closer app x ation is 0b in whicheJ is identified with 30. Taking only a tained by taleing account of the efiects of harsecond approximation by this process v=2ZnJ1 +b2oR J1 b11RJ1e+b02C (6) for the plate voltage and solving the result. In A first approximation similarly gives this expression, J11. is the nth harmonic. of the Jzhb RJ b e (7) plate current, and Zn is the external plateim 1 1+ 01 pedanceto J, In a large number of applications By the trigonometric series (3) a first approximah direct current in the plat Circuit is Ivy-passed tion to; is Jr when Jo is relatively small Rethrough a retard coiLsuch as 5, and only the alplacing J in (7) by J1 and solv ggi s ternating current flows through the output im a I J pedance such as R, via a condenser suchas 10. j fl (3) 20; The output impedance generally is high and fof' a j a a phase in d may be n ed by If the impressed voltage is a pure sinusoidal wave resistance of value R, forall frequencies other H 7 than zero. The D, C. resistance of the retard 9 P coil is, relatively low, and may be considered zero. L -=6 cos pt (10) 26; With these simplifyin assumptions a useful 2P2 1, 2 closer approximation to the fundamental can be J1 1 found. v Subtracting.(8) from (6) leaves The change of the plate current is given by I 2 Peterson and Evans. in their paper referred to 1?" bmRJ2+bz0R bnRjle+bze 3%: above as which from (9), (10) an.d1(11)' becomes J ;b1o1J+bo1e+b2w +b11ve+boze +b3w As a consequence of the definition embodied in I b21v e+b1zve +boae v (1). (3'); thecomponents J2 and J of this expression Wherein the bmn are parameters oi the tube, and ay b parated ey a as given below. wherein v; R z 1,, (2) m 7 4 1 i I 1+bwR) cos 21 st, (14) according to the assumptions previously stated. or since as showjnb I i. ,ythe above mentionedvpaper 4a w harmflmcfi hggher than the thud are r613 of Peterson and Evans, the quantity in brackets twelyrneghglble' in equal to C2,, v i 1 Y J=J@+J1+J2+J3., v 3 i?- '0 50 v ie=.% .1 1251 2 5 successively gab/55x almroxlmatwns to J37 can now beevaluated.- :Subtracting (6) from" in'first order terms, by 212- insecond order terms, nd y .1 n t ird ord r terms.., I lf the cross prodz1 J 1 12 171 03 I (I "1 l-i mRxls z b zo l jljz nRh 30 11 5 Equation (1) may be rewritten replacing v by 3v.

nR li f w fifi -l' os v solving (is), and substituting the; relations (9),

P 'cos The coefficient of P cos 3 pt in Equation (26) is equal to by definition. The fundamental component of this equation is the increment of fundamental caused by the third harmonic, and will be written 8C1P3 cos pt.

Equation (2) then gives for the value of the output voltage.

%RC P cos 2pt%RC P- cos 3pt. (21) The relation between 601 andCs can be calcu- This expression is not tractable to numerical calculation as it contains second derivatives difficult to evaluate. Only first derivatives compose 5. and only second derivatives compose f. It is therefore "desirable to eliminate; from explicitly appearing in the equations connecting 601 and C3, leaving only 5. This is readily accomplished by subtracting (24) from (25) after so treating them as to obtain the same coeflicient for g in both. The result is The ratio of the change in amplitude of the fundamental to the amplitude of the third harmonic can now be found from (27) and (21). It is When C3 is known this relation is readily calculable, requiring only first derivatives.

Determination of the change in fundamental The output impedances of the two tubes are designated by R1 and R2, respectively, forall frequencies except direct current, which meets zero impedance. Let the coefiicients for the first tube be C1 and for the second tube, D1 The output voltage, 6, of the combination without re.- gard to the increment in fundamental or the short-circuited direct current is derived as follows:

If a voltage with an alternating component 6 be applied to the first tube, the alternating component v of the output Voltage will be given by the series wherein the Us are coefficients determined by characteristics of the first tube. The voltage 1)" is the alternating component of thevoltage applied to the grid of the second tube, producing an output voltage 8 determined by the relation where the Ds are coefiicients determined by the characteristics of the second tube. Substituting for 22 its value in terms of e I have To transform this'equation into one which takes account of the change in fundamental it is necessmy to replace throughout and D1 by 1 and (SD 2 L the binomial power series expansion may be used to simplify the result and cross products of the small terms may be dropped. The value of e given by (9) is then substituted in the result, and all direct current products dropped, since they are necessarily zero. There remains for two tubes in cascade by a series of approximations similar to those used for a single tube would be very complicated. Inasmuch as some method applicable to two tubes is useful, notably in repeater circuits, the following expedient may be adopted.

The increment to the fundamental consists of those terms involving P cos pt which have the common multiplier, P This increment comprises three additive terms, the first due to modulation of the complex wave applied to the grid of the second tube, the second due to production by the tween four and five.

first tube of a third'harmonic, and the last due toproduction by the second tube of a third harmonic. The change in fundamental due to any of these contributory causes, or to their combined effect,.can be calculated by means of Equation It is unnecessary in these calculations to know thethird order coefficient provided its ratio to the fundamental is known. This statement applies equally well to a singletube or a two-stage arrangement.

a In Fig. 2 curve A and curve B show the ratio of the change in amplitude of the fundamental to the amplitude of the third harmonic at various load resistances for Western Electric Company tubes of types l04-D and lei-D, respectively, (which are typicallowtubes), with a grid bias of -,,22v volts for the 104-13 tube and 9 volts for the lill-D tube, a filament current of 1.2 am-.

peres for the 104-D tube and 1.1 amperes for the 101-D tube, and a plate voltage of 120 volts for each tube. These ratios were calculated by Equation (28), using computed values of C3 checked experimentally. Ihis coeflicient for the IO i-D tube changes sign within the limits of load resistance used in the calculations, and the ratio becomes infinite for the load resistance at which this change occurs. At this point the increment in fundamental amplitude is 2gP For higher usual values of load resistance the ratio approximates three, the value already mentioned as being applicable when the load impedance is zero to harmonic frequencies. When the plate impedance is matched by the load the ratio is be- The ratio for the 101-D tube departs rapidly from three as the load resistance is increased, and is negative for the higher values considered. It is near unity when the impedances of plate and load are matched.

When the third order coefiicient has the same sign as the fundamental the increment to the fundamental is an increase. When the signs differ the fundamental is decreased by the effects of the harmonics. For the lM-D tube the fundamental amplitude is increased (as distinguished from decreased) for all but very low load resistances. For the 101-13 tube the fundamental is increased for values of load resistance above twice the plate resistance, under the operating conditions assumed. For each of these tubes at value of load resistance can be found such that the fundamental amplitude does not change because of harmonics. This resistance may be found from the curve, and is that value for which the ratio is zero.

Where increment of fundamental caused by harmonics is to be used for obtaining transmission volume expansion or compression, for example, the sign of the increment becomes of interest. The sign can be found from the curves by computing C3 to ascertain whether. the sign of C3 is like or opposite that of the fundamental, or the sign of the fundamental increment can be found by direct measurement of the fundamental increment.

From the foregoing discussion it is seen that the ratio of change in fundamental amplitude to third harmonic, is not a constant, but a function of the load resistance. As the coeficients used vary with plate voltage and grid potential, this ratio is also a function of these. It may be evaluated in any case from measured or calculated values of the third order coefficient, and values of 5, calculated from curves of ,u and R0 as functions of plate voltage.

What is claimed is:

1. An amplifying system comprising a space discharge device having an input circuit and an output circuit, a source of waves tobe amplified associated with said input circuit, and a load associated with said output circuit having its impedance proportioned substantially to a critical value with respect to said discharge device at which value the increment of fundamental waves that is due to harmonics is made substantially zero.

2. Ina space discharge circuit, a space discharge device having electrodes, an input and an output circuit associated with said electrodes, an impedance in said output circuit, means for applying potentials to said electrodes, the values of said impedance and said potentials being proportioned so that the change of fundamental products that is due to harmonics is a minimum.

ROBERT M. KALB. 

